The England international is reportedly a transfer target for the reigning European champions, who come face-to-face with Spurs at the Bernabeu on Tuesday night.
Kane has been in impressive form for club and country this term by scoring 15 goals in all competitions so far, leading to suggestions that Madrid are willing to spend big to land him next summer.
Pochettino has praised the 24-year-old for the "maturity" shown to deal with the ongoing speculation, backing his star striker to remain in North London for the foreseeable future.
"He takes [the rumours] very, very, very naturally," he told AS. "Harry is a boy with a great maturity, with things very clear to him. His dream is to do something big with Tottenham, a club that he's a fan of.
"That important teams recognise his work and that comes out in the media, the only thing that does is encourage him to continue in the form of that time.
"He is an exceptional person, a humble guy with great values in life and as a human, and it gives me great pleasure to train a player like that because it makes my life much easier."